NMR relaxation rate in superconducting pnictides: extended $s_{\pm}$ scenario
D. Parker, O. V. Dolgov, M. M. Korshunov, A. A. Golubov, I. I. Mazin
备注：
5 pages, 4 figures (We have dropped the oversimplified Dynes' model for the unitary limit. Rather, we now treat the Born, unitary, and intermediate regimes on the same footing)
Recently, several measurements of the nuclear spin lattice relaxation rate $T_{1}^{-1}$ in the newly discovered superconducting Fe-pnictides have been reported. These measurements generally show no coherence peak below $T_{c}$ and indicate a low temperature power law behavior, the characteristics commonly taken as evidence of unconventional superconductivity with lines of nodes crossing the Fermi surface. In this work we show that (i) the lack of a coherence peak is fully consistent with the previously proposed nodeless extended $s_{\pm}$-wave symmetry of the order parameter (whether in the clean or dirty limit) and (ii) the low temperature power law behavior can be also explained in the framework of the same model, but requires going beyond the Born model.
We report 19-F NMR investigation of the new high temperature superconductor LaFeAsO(0.89)F(0.11) (Tc ~ 28K). We demonstrate that low frequency spin fluctuations exhibit pseudo gap behavior above Tc. We also deduce the London penetration depth lambda from NMR line broadening below Tc.
In the iron pnictide superconductors, theoretical calculations have consistently shown enhancements of the static magnetic susceptibility at both the stripe-type antiferromagnetic (AFM) and in-plane ferromagnetic (FM) wavevectors. However, the possible existence of FM fluctuations has not yet been examined from a microscopic point of view. Here, using $^{75}$As NMR data, we provide clear evidence for the existence of FM spin correlations in both the hole- and electron-doped BaFe$_2$As$_2$ families of iron-pnictide superconductors. These FM fluctuations appear to compete with superconductivity …
The NMR results in iron pnictides BaFe2(As1-xPx)2 and Ba(Fe1-xCox)2As2 are analyzed based on the self-consistent renormalization (SCR) spin fluctuation theory. The temperature dependence of the NMR relaxation rate (T_1)^{-1} as well as the electrical resistivity is well reproduced by a SCR model where two-dimensional antiferromagnetic (AF) spin fluctuations are dominant. The successful description of the crossover feature from non-Fermi liquid to Fermi liquid behavior strongly suggests that low-lying spin fluctuations in BaFe2(As1-xPx)2 and Ba(Fe1-xCox)2As2 possess an itinerant AF nature, and …
We perform an analysis of the experimentally known temperature dependence of the staggered magnetization in the antiferromagnetic phase. This analysis allows us to put an upper limit on the unknown value of the spin wave velocity along the stripes of equal spin direction (spin stripes). The velocity is about ten times smaller than the velocity perpendicular to the spin stripes. The strongly anisotropic spin-wave dispersion implies a high density of low energy magnetic excitations. We demonstrate that this high density strongly enhances the $^{75}$As NMR spin-lattice relaxation via the Raman sc…
We discuss the novel superconducting characteristics and unusual normal-state properties of iron (Fe)-based pnictide superconductors REFeAsO$_{1-y}$ (RE=La,Pr,Nd) and Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$($T_{c}=$ 38 K) by means of $^{57}$Fe-NMR and $^{75}$As-NQR/NMR. In the superconducting state of LaFeAsO$_{0.7}$ ($T_{c}=$ 28 K), the spin component of the $^{57}$Fe-Knight shift decreases to almost zero at low temperatures, which provide firm evidence of the superconducting state formed by spin-singlet Cooper pairing. The nuclear spin-lattice relaxation rates $(1/T_{1})$ in LaFeAsO$_{0.7}$ and Ba$_…
In Ba(Fe0.95Co0.05)2As2 all of the 75As NMR intensity at the paramagnetic resonance position vanishes abruptly below Tonset(SDW)=56 K, indicating that magnetic (spin density wave) order is present in all of the sample volume, despite bulk superconductivity below Tc=15 K. The two phases thus coexist homogeneously at the microscopic scale. In Ba0.6K0.4Fe2As2, on the other hand, the signal loss below Tonset(SDW)~75 K is not complete, revealing that magnetic order is bound to finite-size areas of the sample, while the remaining NMR signal shows a clear superconducting response below Tc=37 K. Thus,…
In a conventional superconductor, the spin-lattice relaxation rate on all nuclei should have the same temperature dependence below Tc. We performed $^{23}$Na, $^{75}$As, and $^{59}$Co NMR studies on single crystals of NaFe0.95Co0.05As, and found that spin-lattice relaxation rates show very different temperature dependent power-law behavior on three sites. We propose that such site-dependent behavior is due to the facts that the superconductor has two gaps of very different sizes. The power-law exponent of each nucleus is affected by the strength of the hyperfine coupling to the small gap. We a…
NMR longitudinal relaxation rates 1/T1 and Knight shifts K have been measured for superconducting samples of LaFe1-yCoyAsO1-xFx with y=0.0 and 0.0075 and for a nonsuperconducting metallic sample with y=0.1, where the x values are always fixed at 0.11. The temperature (T) dependence the relaxation rates 1/T1 of the superconducting samples has been found to be markedly different from the behavior 1/T1 T^(2.5-3.0) reported by many groups in the entire T range measured (from the temperature immediately below the superconducting transition temperature Tc down to (0.1-0.2)Tc). The nonexistence of th…
The effect of isoelectronic substitutions on the microscopic properties of LaFe1-xRuxAsO, for 0< x< 0.8, has been investigated by means of muSR and 139La NMR. It was found that Ru substitution causes a progressive reduction of the Nèel temperature (T_N) and of the magnetic order parameter without leading to the onset of superconductivity. The temperature dependence of 139La nuclear spin-lattice relaxation rate 1/T_1 can be suitably described within a two-band model. One band giving rise to the spin density wave ground-state, while the other one is characterized by weakly correlated electrons. …
75As NMR and susceptiblity were measured in a Ba(Fe1-xCox)2As2 single crystal for x=6%. Nuclear Magnetic Resonance (NMR) spectra and relaxation rates allow to show that all Fe sites experience an incommensurate magnetic ordering below T=31K. Comparison with undoped compound allows to estimate a typical moment of 0.05 muB. Anisotropy of the NMR widths can be interpreted using a model of incommensurability with a wavevector (1/2-eps,0,l) with eps of the order of 0.04. Below TC=21.8K, a full volume superconductivity develops as shown by susceptibility and relaxation rate, and magnetic order remai…
75As NMR experiments were performed in Ba(Fe1-xRux)2As2 for x=0 to 80%. Magnetic fractions and NMR lineshapes demonstrate that Ru substitution destroys the antiferromagnetic (AF) order inhomogeneously with a magnetic moment distributed from 0.9 to 0 uB. Superconductivity emerges at intermediate Ru doping and coexists with AF order only in the regions where moments are smaller than ~0.3uB, resulting in an original nanoscale texture. This situation contrasts with that of Co substitution, challenging the apparent universality of the phase diagram in Fe-based superconductors.
The unconventional temperature variation of the Knight shift (static spin susceptibility) that has been observed in Fe-based superconductors AFe$_2$As$_2$ (A = K, Rb, Cs) is explained in terms of proximity to a van Hove singularity. Using the Hubbard model we show that when the Fermi energy is in the vicinity of a van Hove singularity, a downturn in spin susceptibility occurs as the temperature is lowered. This behavior is characterized by a temperature, $T^*$, which is determined by the difference in energy between the Fermi level and the van Hove singularity. When vertex corrections are take…
Recent nuclear magnetic resonance (NMR) measurements revealed the coexistence of stripe-type antiferromagnetic (AFM) and ferromagnetic (FM) spin correlations in both the hole- and electron-doped BaFe$_2$As$_2$ families of iron-pnictide superconductors by a Korringa ratio analysis. Motivated by the NMR work, we investigate the possible existence of FM fluctuations in another iron pnictide superconducting family, Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$. We re-analyzed our previously reported data in terms of the Korringa ratio and found clear evidence for the coexistence of stripe-type AFM and FM spin co…
We performed $^{75}$As NMR studies on two overdoped high-quality Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$ (x=0.7 and 1.0) single crystals. In the normal states, we found a dramatic increase of the spin-lattice relaxation ($1/^{75}T_1$) from the x=0.7 to the x=1.0 samples. In KFe$_2$As$_2$, the ratio of $1/^{75}T_1TK_n^2$, where $^{75}K_n$ is the Knight shift, increases as temperature drops. These results indicate the existence of a new type of spin fluctuations in KFe$_2$As$_2$ which is accustomed to being treated as a simple Fermi liquid. In the superconducting state, we observe a step-like feature in t…
75As nuclear magnetic resonance (NMR) experiments were performed on Ba(Fe1-xMnx)2As2 (xMn = 2.5%, 5% and 12%) single crystals. The Fe layer magnetic susceptibility far from Mn atoms is probed by the75As NMR line shift and is found similar to that of BaFe2As2, implying that Mn does not induce charge doping. A satellite line associated with the Mn nearest neighbours (n.n.) of 75As displays a Curie-Weiss shift which demonstrates that Mn carries a local magnetic moment. This is confirmed by the main line broadening typical of a RKKY-like Mn-induced staggered spin polarization. The Mn moment is due…
NMR measurements have been performed on single crystals of Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$ (x = 0, 0.45) and CaFe$_2$As$_2$ grown from Sn flux. The Ba-based pnictide crystals contain significant amounts of Sn in their structure, $\sim 1$%, giving rise to magnetic impurity effects evident in the NMR spectrum and in the magnetization. Our experiments show that the large impurity magnetization is broadly distributed on a microscopic scale, generating substantial magnetic field gradients. There is a concomitant 20% reduction in the transition temperature which is most likely due to magnetic electron…
75As NMR and susceptiblity were measured in a Ba(Fe1-xCox)2As2 single crystal for x=6% for various field H values and orientations. The sharpness of the superconducting and magnetic transitions demonstrates a homogeneity of the Co doping x better than +-0.25%. On the nanometer scale, the paramagnetic part of the NMR spectra is found very anisotropic and very narrow for H//ab which allows to rule out the interpretation of Ref.[6] in terms of strong Co induced electronic inhomogeneities. We propose that a distribution of hyperfine couplings and chemical shifts due to the Co effect on its nearest…
We report muon-spin relaxation measurements of highly homogeneous samples of FeAs and FeAs2, both previously found as impurity phases in some samples of recently synthesized pnictide superconductors. We observe well defined muon precession in the FeAs sample with two precession frequencies of 38.2(3) and 22.7(9) MHz at 7.5 K, with the majority of the amplitude corresponding to the lower frequency component. In FeAs2 we confirm previous measurements showing that no long-ranged magnetic order occurs above 2 K and measure the muon spin relaxation rate, which increases on cooling. Our results excl…
Systematic P-NMR studies on LaFe(As_{1-x}P_x)(O_{1-y}F_y) with y=0.05 and 0.1 have revealed that the antiferromagnetic spin fluctuations (AFMSFs) at low energies are markedly enhanced around x=0.6 and 0.4, respectively, and as a result, Tc exhibits respective peaks at 24 K and 27 K against the P-substitution for As. This result demonstrates that the AFMSFs are responsible for the increase in Tc for LaFe(As_{1-x}P_x)(O_{1-y}F_y) as a primary mediator of the Cooper pairing. From a systematic comparison of AFMSFs with a series of (La_{1-z}Y_z)FeAsO_δ compounds in which Tc reaches 50 K for z=0.95,…
We consider a two-band superconductor with relative phase $π$ between the two order parameters as a model for the superconducting state in ferropnictides. Within this model we calculate the microwave response and the NMR relaxation rate. The influence of intra- and interband impurity scattering beyond the Born and unitary limits is taken into account. We show that, depending on the scattering rate, various types of power law temperature dependencies of the magnetic field penetration depth and the NMR relaxation rate at low temperatures may take place.
The experimental consequences of different order parameters in iron-based superconductors are theoretically analyzed. We consider both nodeless and nodal order parameters, with an emphasis on the $\cos(k_x)\cdot \cos(k_y)$ nodeless order parameter recently derived by two of us. We analyze the effect of this order parameter on the spectral function, density of states, tunneling differential conductance, penetration depth, and the NMR spin relaxation time. This extended s-wave symmetry has line-zeroes in between the electron and hole pockets, but they do not intersect the two Fermi surfaces for …
Observation of an anomalous temperature dependence of the spin susceptibility, along with a spin gap in NMR, in the quantum paramagnetic normal state of Iron Pnictides is a signature of an unusual metallic state. We argue that both these anomalous features are associated with a wide fluctuational regime dominated by dynamical, short-ranged and frustrated spin correlations in a strongly correlated metal. Using LDA+DMFT, we show that both these features can be quantitatively undertstood in the doped Fe-pnictides. We argue that such spin correlations naturally arise in a Mottness scenario, where …
In copper-oxide and iron-based high temperature (high-$T_{\rm c}$) superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron-pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\rm s}$ coincides with the magnetic transition temperature $T_{\rm N}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\rm s}$ = 54 K is well separated from $T_{\rm N}$ = 42…
We investigate the quasiparticle relaxation and low-energy electronic structure in undoped SrFe_2As_2 exhibiting spin-density wave (SDW) ordering using optical pump-probe femtosecond spectroscopy. A remarkable critical slowing down of the quasiparticle relaxation dynamics at the SDW transition temperature T_SDW = 200K is observed. From temperature dependence of the transient reflectivity amplitude we determine the SDW-state charge gap magnitude, 2Delta_SDW/k_BT_SDW=7.2+-1. The second moment of the Eliashberg function, lambda<(hbar omega)^2>=110+-10meV^2, determined from the relaxation time abo…
This study leads to the investigation of the non-equilibrium electron relaxation in the normal state of iron pnictides. Here we consider the relaxation of electrons due to their coupling with magnons and phonons in the metallic state of iron pnictides using the memory function approach. In the present model, electrons live at a higher temperature than that of the phonon and magnon baths, mimicking a non-equilibrium steady state situation. Further we analyze theoretically the generalized Drude scattering rate within the framework of Two Temperature Model and study the full frequency and tempera…
We report muon-spin relaxation measurements on SrFeAsF, which is the parent compound of a newly discovered iron-arsenic-fluoride based series of superconducting materials. We find that this material has very similar magnetic properties to LaFeAsO, such as separated magnetic and structural transitions (TN = 120 K, Ts = 175 K), contrasting with SrFe2As2 where they are coincident. The muon oscillation frequencies fall away very sharply at TN, which suggests that the magnetic exchange between the layers is weaker than in comparable oxypnictide compounds. This is consistent with our specific heat m…
High-temperature superconductivity in Fe-based pnictides and chalcogenides has been one of the most significant recent discoveries in condensed matter physics and has attracted remarkable attention in the last decade. These materials are characterized by a complex fermiology and, as a result, feature a wide range of electronic properties as a function of different tuning parameters such as chemical doping, temperature and pressure. Along the path towards the comprehension of the physical mechanisms underlying this rich phenomenology, NMR (nuclear magnetic resonance) and NQR (nuclear quadrupole…
Doping dependence of the spin fluctuations and the electron correlations in the effective five-band Hubbard model for iron pnictides is investigated using the fluctuation-exchange approximation. For a moderate hole doping, we find a dominant low-energy spin excitation at Q=(π,0), which becomes critical at low temperature. The low-energy spin excitations in the heavily hole-doped region are characterized by weak Q dependence. The electron doping leads to an appearance of a pseudogap in spin excitation spectrum. Correspondingly, the NMR-1/T1 relaxation rate is strongly enhanced on the hole-doped…
Impurity nuclear spin relaxation is studied theoretically. A single impurity generates a bound state localized around the impurity atom in unconventional superconductors. With increasing impurity potential, the relaxation rate $T_1^{-1}$ is reduced by the impurity potential. However, it has a peak at low temperatures due to the impurity bound state. The peak disappears at non-impurity sites. The impurity site NMR measurement detecting a local electronic structure just on the impurity atom is very useful for identifying the unconventional pairing states.
Site-dependent NMR relaxation time $T_1({\bf r})$ is calculated in the vortex state using the Bogoliubov-de Gennes theory, taking account of possible "field-induced stripe'' states in which the magnetism arises locally around a vortex core in d-wave superconductivity. The recently observed huge enhancement $T_1^{-1}({\bf r})$ below $T_c$ at a core site in Tl$_2$Ba$_2$CuO$_6$ is explained. The field-induced stripe picture explains consistently other relevant STM and neutron experiments.
We report systematic ^{75}As-NQR and ^{139}La-NMR studies on nickel-pnictide superconductors LaNiAsO_{1-x}F_x (x=0, 0.06, 0.10 and 0.12). The spin lattice relaxation rate 1/T_1 decreases below T_c with a well-defined coherence peak and follows an exponential decay at low temperatures. This result indicates that the superconducting gap is fully opened, and is strikingly different from that observed in iron-pnictide analogs. In the normal state, 1/T_1T is constant in the temperature range T_c \sim 4 K < T <10 K for all compounds and up to T=250 K for x=0 and 0.06, which indicates weak electron c…
We studied the quantum critical behavior of the second antiferromagnetic (AF) phase in the heavily electron-doped high-$T_c$ pnictide, LaFeAsO$_{1-x}$H$_x$ by using $^{75}$As and $^{1}$H nuclear-magnetic-resonance (NMR) technique. In the second AF phase, we observed a spatially modulated spin-density-wave-like state up to $x$=0.6 from the NMR spectral lineshape and detected a low-energy excitation gap from the nuclear relaxation time $T_1$ of $^{75}$As. The excitation gap closes at the AF quantum critical point (QCP) at $x \approx 0.49$. The superconducting (SC) phase in a lower-doping regime …
Nuclear magnetic relaxation rate 1/T_1 in iron-pnictide superconductors is calculated using the gap function obtained in a microscopic calculation. Based on the obtained results, we discuss the issues such as the rapid decrease of 1/T_1 just below the transition temperature and the difference between nodeless and nodal s-wave gap functions. We also investigate the effect of Coulomb interaction on 1/T_1 in the random phase approximation and show its importance in interpreting the experimental results.
A new mechanism for relaxing the nuclear magnetic moments, in which a pair of spin-polarized BCS quasiparticles is emitted or absorbed, and which dominates at low temperature, is identified in type-II d-wave superconductors in an external magnetic field above Hc1. The results of the theory are compared with the NMR experiments on YBCO in high magnetic fields and found to agree without invoking antiferromagnetic order in the vortex core.
We report the 75As nuclear magnetic resonance (NMR) measurement of the hole-doped superconductor Ba1-xKxFe2As2 with different lattice parameters and different superconducting volume fractions (Tc = 38K). 75As-NMR spectra revealed that the magnetically ordered and superconducting phases are microscopically separated. The spin-lattice relaxation rate 1/T1 in the normal state reflects the existence of a large two-dimensional antiferromagnetic spin fluctuation. The 1/T1 in the superconducting state down to the lowest measurement temperature T varies close to T^3. In addition, it exhibits no cohere…
An unusual successive phase transition from superconducting (SC) to antiferromagnetic (AF) phases was discovered via ^{75}As and ^{27}Al nuclear magnetic resonance (NMR) in (Fe_2As_2)(Ca_6(Al, Ti)_4O_y) with four (Al, Ti)O layers intercalated between FeAs planes. Although the spatially-uniform AF ordering is clearly visible from ^{27}Al spectra, the ordered moments are very small and the low-frequency fluctuation is much suppressed, contrary to existing pnictides with localized magnetic elements. Furthermore, the temperature (T) dependence of the fluctuation at both nuclei is very similar thro…
We report the first ^{75}As-NMR study on a single crystal of the hole-doped iron-pnictide superconductor Ba_{0.7}K_{0.3}Fe_2As_{2} (T_c = 31.5 K). We find that the Fe antiferromagnetic spin fluctuations are anisotropic and are weaker compared to underdoped copper-oxides or cobalt-oxide superconductors. The spin lattice relaxation rate 1/T_1 decreases below T_c with no coherence peak and shows a step-wise variation at low temperatures, which is indicative of multiple superconducting gaps, as in the electron-doped Pr(La)FeAsO$_{1-x}$F$_{x}$. Furthermore, no evidence was obtained for a microscopi…
We systematically investigate temperature- and spectrally-dependent optical reflectivity dynamics in AAs$_{2}$Fe$_{2}$, (A=Ba, Sr and Eu), iron-based superconductors parent spin-density-wave (SDW) compounds. Two different relaxation processes are identified. The behavior of the slower process, which is strongly sensitive to the magneto-structural transition, is analyzed in the framework of the relaxation-bottleneck model involving magnons. The results are compared to recent time resolved angular photoemission results (TR-ARPES) and possible alternative assignment of the slower relaxation to th…
We discuss the nuclear magnetic relaxation rate and the superfluid density with the use of the effective five-band model by Kuroki et al. [Phys. Rev. Lett. 101, 087004 (2008)] in Fe-based superconductors. We show that a fully-gapped anisotropic \pm s-wave superconductivity consistently explains experimental observations. In our phenomenological model, the gaps are assumed to be anisotropic on the electron-like βFermi surfaces around the M point, where the maximum of the anisotropic gap is about four times larger than the minimum.
We present a phenomenological theory of quasiparticle scattering and transport relaxation in the normal state of iron pnictides based on the simplified two-band model coupled via spin fluctuations. In analogy with anomalous properties of cuprates it is shown that a large and anomalous normal-state resistivity and thermopower can be interpreted as the consequence of strong coupling to spin fluctuations. The generalization to the superconducting phase is also discussed.
Measurements of the electrical resistivities, Hall coefficients, thermoelectric powers, electronic specific heat coefficients have been carried out for samples of LnFe1-yMyAsO1-xFx (Ln=La, Nd; M=Co, Mn; x=0.11) obtained by M atom dopings to the superconducting LnFeAsO1-xFx (Ln1111) system. The NMR longitudinal relaxation rates 1/T1 have also been measured for samples of LaFe1-yCoyAsO1-xFx with various x values. Co atoms doped to the superconducting LnFeAsO1-xFx are nonmagnetic, and the Tc-suppression by the Co atoms has been found to be too weak to understand by the pair breaking effect expect…
Magnetization and 63Cu NMR-NQR relaxation measurements are used to study the superconducting fluctuations in YBa2Cu3O6+x (YBCO) oriented powders. In optimally doped YBCO the fluctuating negative magnetization M_{fl}(H,T) is rather well described by an anisotropic Ginzburg-Landau (GL) functional and the curves M_{fl}/sqrt{H} cross at Tc. In underdoped YBCO, instead, over a wide temperature range an anomalous diamagnetism is observed, stronger than in the optimally doped compound by about an order of magnitude. The field and temperature dependences of M_{fl} cannot be described either by an anis…
The electron spin resonance absorption spectrum of Eu^{2+} ions serves as a probe of the normal and superconducting state in Eu_{0.5}K_{0.5}Fe_2As_2. The spin-lattice relaxation rate 1/T_1^{\rm ESR} obtained from the ESR linewidth exhibits a Korringa-like linear increase with temperature above T_C evidencing a normal Fermi-liquid behavior. Below 45 K deviations from the Korringa-law occur which are ascribed to enhanced magnetic fluctuations within the FeAs layers upon approaching the superconducting transition. Below T_C the spin-lattice relaxation rate 1/T_1^{\rm ESR} follows a T^{1.5}-behavi…
We employ the phenomenological theory of the quasiparticle relaxation based on the simplified two-band description and the spin-fluctuation induced interband coupling to analyze recent normal-state transport data in electron-doped iron pnictides, in particular the Ba(Fe_1-x Co_x)_2As_2 family. Temperature dependence of the resistivity, thermopower and the Hall constant are evaluated. It is shown that their anomalous behavior emerging from experiments can be consistently described within the same framework assuming also non-Fermi-liquid spin fluctuations.
Nonequilibrium quasiparticle relaxation dynamics is reported in superconducting CaFe1.89Co0.11As2 single crystal using femtosecond time-resolved pump-probe spectroscopy. The carrier dynamics reflects a three-channel decay of laser deposited energy with characteristic time scales varying from few hundreds of femtoseconds to order of few nanoseconds where the amplitudes and time-constants of the individual electronic relaxation components show significant changes in the vicinity of the spin density wave (T_SDW ~ 85 K) and superconducting (T_SC ~ 20 K) phase transition temperatures. The quasipart…
The spin-lattice relaxation rate of nuclear magnetic resonance in a clean superconductor without inversion center is calculated for arbitrary pairing symmetry and band structure, in the presence of strong spin-orbit coupling.
We have performed 75As Nuclear Magnetic Resonance (NMR) measurements on aligned powders of the new LaO0.9F0.1FeAs superconductor. In the normal state, we find a strong temperature dependence of the spin shift and Korringa behavior of the spin lattice relaxation rate. In the superconducting state, we find evidence for line nodes in the superconducting gap and spin-singlet pairing. Our measurements reveal a strong anisotropy of the spin lattice relaxation rate, which suggest that superconducting vortices contribute to the relaxation rate when the field is parallel to the c-axis but not for the p…
We numerically study the spatially-resolved NMR around a single vortex in a noncentrosymmetric superconductor such as CePt3Si. The nuclear spin-lattice relaxation rate 1/T1 under the influence of the vortex core states is calculated for an s+p-wave Cooper pairing state. The result is compared with that for an s-wave pairing state.
This article reviews the NMR and NQR studies on iron-based high-temperature superconductors by the IOP/Okayama group. It was found that the electron pairs in the superconducting state are in the spin-singlet state with multiple fully-opened energy gaps. The antiferromagnetic spin fluctuations in the normal state are found to be closely correlated with the superconductivity. Also the antiferromagnetic spin fluctuations are anisotropic in the spin space, which is different from the case in copper oxide superconductors. This anisotropy originates from the spin-orbit coupling and is an important r…
We calculate the NMR relaxation rate due to quadrupolar coupling of the nucleus to a local, strongly anharmonic phonon mode. As a model potential for a rattling motion we consider a square-well potential. We calculate the free phonon Green's function analytically and derive the low and high temperature limits of the NMR relaxation rate. It is shown that the temperature dependence of the NMR relaxation rate possesses a peak in contrast to harmonic phonons but in qualitative agreement with a recent NMR study on KOs2O6. We discuss the influence of phonon renormalization due to electron-phonon int…
We report a comprehensive study of the noncentrosymmetric NbReSi superconductor by means of muon-spin rotation and relaxation ($μ$SR) and nuclear magnetic resonance (NMR) techniques. NbReSi is a bulk superconductor with $T_c = 6.5$ K, characterized by a large upper critical field, which exceeds the Pauli limit. Both the superfluid density $ρ_\mathrm{sc}(T)$ (determined via transverse-field $μ$SR) and the spin-lattice relaxation rate $T_1^{-1}(T)$ (determined via NMR) suggest a nodeless superconductivity (SC) in NbReSi. We also find signatures of multigap SC, here evidenced by the field-depende…
We study the spin-lattice relaxation rate of nuclear magnetic resonance in a two-band superconductor. Both conventional and unconventional pairing symmetries for an arbitrary band structure in the clean limit are considered. The importance of the inter-band interference effects is emphasized. The calculations in the conventional case with two isotropic gaps are performed using a two-band generalization of Eliashberg theory.
The dependence of the Maki-Thompson (MT) and of the density of states depletion (DOS) contributions from superconducting fluctuations (SF) to NMR-NQR relaxation is derived in the framework of the diagrammatic theory, applied to layered three dimensional (3D) high T_c superconductors. The regularization procedure devised for the conductivity (Buzdin and Varlamov, Phys. Rev. B, 58, 14195 (1998)) is used in order to avoid the divergence of the DOS term. The theoretical results are discussed in the light of NMR-NQR measurements in YBCO and compared with the recent theory (Eschrig et al., Phys. Rev…
The temperature dependence of the site-dependent nuclear spin relaxation time T_1 around vortices is studied in s-wave and d-wave superconductors.Reflecting low energy electronic excitations associated with the vortex core, temperature dependences deviate from those of the zero-field case, and T_1 becomes faster with approaching the vortex core. In the core region, T_1^{-1} has a new peak below T_c. The NMR study by the resonance field dependence may be a new method to prove the spatial resolved vortex core structure in various superconductors.
We discuss the type of pairing in the hexagonal pnictide superconductor SrPtAs, taking into account its multiband structure. The topological chiral $d$-wave state with time-reversal-symmetry breaking has been anticipated from the spontaneous magnetization observed by the muon-spin-relaxation experiment. We point out in this paper that the recent experimental reports on the nuclear-spin-lattice relaxation rate $T_1^{-1}$ and superfluid density $n_s(T)$, which seemingly support the conventional $s$-wave pairing, are also consistent with the chiral $d$-wave state. The compatibility of the gap and…
Nuclear magnetic resonance (NMR) provides local, bulk information about the electronic properties of materials, and it has been influential for theory of high-temperature superconducting cuprates. Importantly, NMR found early that nuclear relaxation is much faster than what one expects from coupling to fermionic excitations above the critical temperature for superconductivity ($T_{\rm c}$), i.e. what one estimates from the Knight shift with the Korringa law. As a consequence, special electronic spin fluctuations have been invoked. Here, based on literature relaxation data it is shown that the …
We study the vortex-dynamics of a BaFe{1.82}Ni_{0.18}As_2 crystal with Tc = 8 K, by measuring flux-creep over the second magnetisation (or fish-tail) peak for both H//c-axis and H//ab planes. Magnetic relaxation data show an anomalously long initial stage of relaxation, lasting approximately10 minutes for H//c-axis and 2-3 min for H//ab, resembling a transient effect with a lower relaxation rate, which is followed by the usual log(time) relaxation. Interestingly, study of the relaxation rate R vs H for both stages of relaxation and for both field directions, are featureless over the field rang…
The doping dependence of spin excitations in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ is studied based on a two-orbital model under RPA approximation. The interplay between the spin-density-wave (SDW) and superconductivity (SC) is considered in our calculation. Our results for the spin susceptibility are in good agreement with neutron scattering (NS) experiments in various doping ranges at temperatures (T) above and below the superconducting transition temperature T$_{c}$. For the overdoped sample where one of the two hole pockets around $Γ$ point disappears according to ARPES, we show that the im…
We calculate the effect of nonmagnetic impurity scattering on the spin-lattice relaxation rate in two-band superconductors with the s-wave pairing symmetry. It is found that for the interaction parameters appropriate for MgB2 the Hebel-Slichter peak is suppressed by disorder in the limit of small interband impurity scattering rate. In the limit of strong impurity scattering, when the gap functions in the two bands become nearly equal, the single-band behavior is recovered with a well-defined coherence peak just below the transition temperature.
We calculate ab initio the NMR relaxation rates and the Knight shifts in MgB_2. We show that the dominant relaxation mechanism at the B nucleus is the interaction with the electronic orbital moment, and we give a simple explanation of that using a simple $sp$ tight binding model. When Stoner enhancement (also calculated ab-initio) is accounted for, we obtain good agreement with reported experimental values. For the 25Mg nucleus, we predict that the dominant relaxation mechanism is the Fermi-contact interaction, which also dominates the Mg Knight shift.
